Topological Signatures in Nodal Semimetals through Neutron Scattering

Topological nodal semimetals are known to host a variety of fascinating electronic properties due to the topological protection of the band-touching nodes. Neutron scattering, despite its power in probing elementary excitations, has not been routinely applied to topological semimetals, mainly due to the lack of an explicit connection between the neutron response and the signature of topology. In this work, we theoretically investigate the role that neutron scattering can play to unveil the topological nodal features: a large magnetic neutron response with spectral non-analyticity can be generated solely from the nodal bands. A new formula for the dynamical structure factor for generic topological nodal metals is derived. For Weyl semimetals, we show that the locations of Weyl nodes, the Fermi velocities and the signature of chiral anomaly can all leave hallmark neutron spectral responses. Our work offers a neutron-based avenue towards probing bulk topological materials.

Single-particle excitations and metal-insulator transition of ultracold Fermi atoms in one-dimensional optical lattice with spin-orbit coupling

The dynamic structure factors reflecting the excitation spectra were investigated in a one-dimensional (1D) optical lattice with a spin-orbit coupling (SOC) effect. The results reveal that the single-particle excitations of both the density and spin dynamical structure factors are strongly reconstructed and split owing to the SOC effect, and a hat-like excitation band appears in the high-binding-energy region. The hat-like excitation band of the density dynamical structure factor exhibits an arc form, and has a pocket in the spin dynamical structure factor. In particular, only a gapless single-particle excitation point is left for both the density dynamical structure factor and spin dynamical structure factor when the SOC strength reaches a critical point at half-filling. A stronger SOC strength causes the gapless excitation points to disappear, which indicates that metal-insulator transition occurs. The metal-insulator transition only appears in half-filling and lightly doped regimes.

A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model

We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a 1/c1/c expansion. The n^\mathrm{th}nth term of the expansion is of order 1/c^n1/cn and takes into account all \lfloor \tfrac{n}{2}\rfloor+1⌊n2⌋+1 particle-hole excitations over the averaging eigenstate. Importantly, in contrast to a "bare" 1/c1/c expansion it is uniform in space and time. The framework is based on a method for taking the thermodynamic limit of sums of form factors that exhibit non integrable singularities. We expect our framework to be applicable to any local operator. We determine the first three terms of this expansion and obtain an explicit expression for the density-density dynamical correlations and the dynamical structure factor at order 1/c^21/c2. We apply these to finite-temperature equilibrium states and non-equilibrium steady states after quantum quenches. We recover predictions of (nonlinear) Luttinger liquid theory and generalized hydrodynamics in the appropriate limits, and are able to compute sub-leading corrections to these.

Dynamical structure factors of dynamical quantum simulators

The dynamical structure factor is one of the experimental quantities crucial in scrutinizing the validity of the microscopic description of strongly correlated systems. However, despite its long-standing importance, it is exceedingly difficult in generic cases to numerically calculate it, ensuring that the necessary approximations involved yield a correct result. Acknowledging this practical difficulty, we discuss in what way results on the hardness of classically tracking time evolution under local Hamiltonians are precisely inherited by dynamical structure factors and, hence, offer in the same way the potential computational capabilities that dynamical quantum simulators do: We argue that practically accessible variants of the dynamical structure factors are bounded-error quantum polynomial time (BQP)-hard for general local Hamiltonians. Complementing these conceptual insights, we improve upon a novel, readily available measurement setup allowing for the determination of the dynamical structure factor in different architectures, including arrays of ultra-cold atoms, trapped ions, Rydberg atoms, and superconducting qubits. Our results suggest that quantum simulations employing near-term noisy intermediate-scale quantum devices should allow for the observation of features of dynamical structure factors of correlated quantum matter in the presence of experimental imperfections, for larger system sizes than what is achievable by classical simulation.